II.3. DETERMINATION OF THE ELECTRON SPECIFIC CHARGE BY MEANS OF THE MAGNETRON METHOD

Transcription

1 II.3. DETEMINTION OF THE ELETON SPEIFI HGE Y MENS OF THE MGNETON METHOD. Wok pupos Th wok pupos is to dtin th atio btwn th absolut alu of th lcton chag and its ass, /, using a dic calld agnton. In this dic, th tajctois of th lctons ittd by a hatd filant a odifid by an xtnally applid agntic fild.. Thoy Th thod to dtin th lcton spcific chag / is basd on th study of th lcton ont in lctic and agntic filds. Th foc acting upon a paticl of chag q und ths filds is calld Lontz foc and is gin by th foula: F E +, () ( ) wh is th lcton locity, E is th lctic fild intnsity, and is th agntic fild induction. ccoding to Nwton s scond law: F a, () th quation of th lcton ont is of th fo: d ( E + ). (3) dt To dtin th lcton spcific chag, w will us th agnton thod. Th agnton is a cylindically sytic acuu diod, placd insid a concntic solnoidal coil. Its sction is psntd in Figu. Th cathod, fod by a wi that also ss as filant, is coaxial with th cylindical anod and with th coil S, so that th agntic fild induction cto is paall with th agnton syty axis. 69

2 Figu. Whn, th lctons ittd by th cathod though tholctonic ission, will o adially towads th anod und th influnc of th lctic fild E poducd by th bias U applid to th tub. Whn, th lctons suff a diation othogonal to, du to th agntic fild. Thi tajctois, stating fo th cathod and nding on th anod, cu thslfs. If th agntic fild bcos gat nough, thn it is possibl that th lctons can n ach th anod. This happns whn thi tajctois bco cicula, with th adius /. In this situation th lctons fo a spac chag gion aound th cathod, scning it, and th anodic cunt pactically dops to zo. W will ty to find out a lation that will gi us th xpssion of th lcton spcific chag /, stating fo this xpintal situation. Du to th agnton syty, w will us cylindical coodinats, θ, z, so that E E u and uz.th unitay ctos u, uθ, a not constant (s Figu ), but a gin by th lations u cos θ u + sin θ u, uθ sin θ u + cos θ u, (4) x y so that thi ti diatis a u& θ& uθ, u& θ&. (5) Th locity is thn u x y 7

3 & u + θ& uθ + z& (6) u z and th ctoial Equation (3) taks th fo && θ& E θ&, (7) & θ & + && θ &, (8) & z&. (9) Figu. To find out th lcton tajctoy, w will suppos that th ti dpndnc of any quantity is iplicit though th ti dpndnc of th adius, that is d dt Thn Equation (8) bcos d &. () d dθ & + θ&, () d which has th solution θ& +. () To find out th intgation constant, w will suppos that th lctons a ittd othogonal to th cathod sufac (this assuption is suppotd by th action of th iag foc that appas whn a chag is clos to a tallic sufac), so that 7

4 7 ( ) u, (3) bing th cathod adius. Fo this condition w obtain θ & (4) and also, fo Equation (9), z&. (5) s d dv E, (6) wh V is th potntial, th lation (7) will gi 4 d dv d d &. (7) Und th conditions (3) and ( ) ( ) U V V,, (8) th solution of Equation (7) is 4 + V &. (9) t th anod adius, 4 + U &. () This ans that th only lctons that can ach th anod a thos fo which th ight hand sid of Eq. () is non-ngati. If, this ans 8 8 U U () (as << ). Othwis, w nd

5 ( ) in 4. () Fo quation () w also obtain th lcton spcific chag as 8U. (3) Th conduction lctons in tals a dscibd by th Fi-Diac statistics. How, as th xtaction wok is uch gat than th thal ngy k T, th ittd lctons oby a Maxwll-oltzann statistics, () n xp. (4) k lthough this lation is not consistnt with th assuption (3), it gis us a good dsciption of th ittd lctons bhaiou. s long as <, all th ittd lctons ach th anod, so that Whn, () i i Sn d i in 3 3 xp d. (5) k xp d, (6) k so that w obtain wh [ + ( )] [ ( )] i i, (7) xp 8k. (8) 8k s th agntic fild induction fo a coil is 73

6 w can wit N µ ni µ I, (9) l [ + D( I I )] [ D( I I )] i i, (3) xp µ D n, (3) 8 U U. K. (3) µ n I I Th logaith of quation (3) is Whn this bcos so that i log i i log i ( I ) log [ + D( I I )] D I. (33) D ( I ) << < D I, (34) 3 D ( I I ) ( I I ) D ( I I ) ( I I ) +..., (35) i D log, (36) i 3 which psnts an alost staight lin. Th cosponding gaph is psntd in Figu 3. On can s that, using this function th dtination of I is ath asy. Th alu of th constant K is wll dtind in ach xpintal cas (whn n and a known) and ust b xpssd in I.S., so that, by placing th oltag U (in olts) and th cunt I (in aps), w obtain th spcific chag / (in /kg). Fo th dic usd in th psnt wok, th alu of th constant is K,5 ( I. S.). 9 74

7 3. Expintal st-up Figu 3. Figu 4. Th daft of th xpintal st-up, psntd in Figu 4, is coposd of two cicuits : in th lft pat is th cicuit of th tub and in th igth pat th on of th solnoid.this includs: - Th agnton tub, T. - Th solnoid, S. - Th oltt V, to asu th oltag applid to th tub. - Th illiat, to asu th anodic cunt; w will us th scal of.6. - Th at, to asu th solnoid cunt; w will us th scal of.6. - Th hostats and, usd as potntiots. - Th switchs K and K. 4. Woking Pocdu Th abo st-up is ntily assbld on a wok bd and is fdd fo th ntwok though a d.c. ctifi. y tuning on th switchs K 75

8 and K, both cicuits will ha a oltag such that with th potntiot w can ay th oltag U applid to th tub and with th potntiot w can ay th cunt I that flows though th solnoid Th asunt of th anodic cunt i in od to obtain th alu I is ad by kping th bias U constant. Th aiation stps fo th cunt I a chosn such that th adings on th illiat scal could b ad with th highst possibl accuacy (i.. 5 ).Th asunts ust b pfod fo th diffnt alus of th bias, U < U < U 3, connintly chosn. Th sults will b wittn down in Tabl. Tabl U I()... 3V i()... U I()... 4V i()... U 3 I()... 5V i() Expintal data pocssing Fo th th diffnt alus of th oltag, U, U, U 3, on plots th gaphs log( i) f ( I ) i (s Figu 3). Th distinct alus will b obtaind in this way fo I,cosponding to th th alus of th bias U, fo which / is to b coputd accoding to th lation (3). Th aag of th th obtaind alus / is considd to b th closst sult to th al alu. 6. Qustions. How do th lctons o, copad to th diction of th xtnal applid lctic fild E?. How do th lctons o apotd to th diction of th agntic induction? 3. What is th physical aning of th lation (9)? 76